
where \(\mathbf {\mathrm {R}}_{i}^{\prime (u)}\)  is the rank-\((M\!-\!1)\)  SCM estimated by ILRMA,
\(\mathbf {b}_{i}\)  is the unit eigenvector of \(\mathbf {\mathrm {R}}_{i}^{\prime (u)}\)  that corresponds to the zero eigenvalue,
\(\lambda _{i}\)  is a scalar variable, and \(^{\mathsf {H}}\)  denotes the Hermitian transpose.
Equation (REF ) applies back-projection [1]} to \(M-1\)  diffuse noise components (estimates)
and calculates the sum of the \(M-1\)  resultant SCMs.
Thus, we fix both the spatial basis of the directional target source \(\mathbf {a}_{i}^{(h)}\) 
and the rank-\((M\!-\!1)\)  SCM \(\mathbf {\mathrm {R}}_{i}^{\prime (u)}\) .
The full-rank SCM \(\mathbf {\mathrm {R}}_{i}^{(u)}\)  can be recovered by estimating the residual eigenvalue \(\lambda _{i}\) .
Also, the variances of the directional target source and diffuse noise, \(r_{ij}^{(h)}\)  and \(r_{ij}^{(u)}\) , respectively, are simultaneously estimated.
